This just tells WP to get the posts ordered according to their ‘menu_order’ position. Therefore you can get the posts ordered anytime you use a function such as get_posts simply by giving it the required arguments:

<?php get_posts('orderby=menu_order&order=ASC'); ?>

Checkout the get_posts() function in the wordpress codex for more info.
Note that it says menu_order is only useful for pages, posts have a menu_order position too, it just isn’t used. postMash provides you with an iterface so that you can use it.